JOINT RESEARCH CENTER FOR PANEL STUDIESDISCUSSION PAPER SERIES
DP2009-002
August, 2009

Community Rating, Cross Subsidies and Underinsurance: Why So Many
Households in Japan Do Not Purchase Earthquake InsuranceMichio Naoi*
Miki Seko**Kazuto Sumita***
Abstract
A theoretical framework and empirical evidence are presented to show the connection between
community uniform rating and cross-subsidies in earthquake insurance policy in Japan.
Cross-subsidies are defined as the difference between a fair actuarial premium and the community
uniform rate. The estimation result shows that the uniform community rating may unintentionallycross-subsidize inhabitants in high risk areas at the expense of inhabitants in low risk areas. Our
simulation results indicate that replacing the current community rating with the fair actuarial
premium would increase the overall subscription rate for earthquake insurance by about 3.7
percentage point, and that the increase is particularly prominent in relatively less risky areas. We
propose modifying the Japanese earthquake insurance system by adopting a more refined risk rating
system that more closely reflects regional differences in earthquake risk.

*Michio Naoi
Faculty of Economics, Keio University** Miki Seko

Faculty of Economics, Keio University*** Kazuto Sumita

Department of Economics, Kanazawa Seiryo University

Joint Research Center for Panel Studies
Keio University

Community Rating, Cross Subsidies and Underinsurance: Why So Many
Households in Japan Do Not Purchase Earthquake Insurance *First draft: April 27, 2008 / First revision: June 7, 2008
Second revision: June 29, 2008 / Third revision: October 13, 2008
Fourth revision: May 10, 2009
Michio Naoia, Miki Sekob† , Kazuto Sumitac
a. Faculty of Economics, Keio University, Mita Toho Bldg. 5th Floor, 3-1-7 Mita, Minato-ku,
Tokyo, 108-0073, Japanb. Faculty of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japanc. Department of Economics, Kanazawa Seiryo University, Ushi 10-1, Gosho-machi,
Kanazawa-shi, Ishikawa, 920-8620, Japan

Abstract
A theoretical framework and empirical evidence are presented to show the connection
between community uniform rating and cross-subsidies in earthquake insurance policy inJapan. Cross-subsidies are defined as the difference between a fair actuarial premium andthe community uniform rate. The estimation result shows that the uniform community
rating may unintentionally cross-subsidize inhabitants in high risk areas at the expense of
inhabitants in low risk areas. Our simulation results indicate that replacing the current
community rating with the fair actuarial premium would increase the overall subscription
rate for earthquake insurance by about 3.7 percentage point, and that the increase isparticularly prominent in relatively less risky areas. We propose modifying the Japanese
earthquake insurance system by adopting a more refined risk rating system that moreclosely reflects regional differences in earthquake risk.
JEL classification: D81, G22, G28, R10.
Keywords: Earthquake insurance, Cross-subsidization, Risk, Japan.
*

We are grateful to the National Research Institute for Earth Science and Disaster Prevention (NIED) for
generously providing us with the data on earthquake hazard information. We also thank K. W. Chau,
Dwight M. Jaffee, an anonymous referee and participants at the Asia-Pacific Real Estate Research
Symposium (APRES) for their helpful comments and suggestions. The first author (Michio Naoi)
acknowledges a Grant-in-Aid (#19730183) for Young Scientists (B) from the Ministry of Education,
Culture, Sports, Science and Technology. Also, the second and third authors (Miki Seko and Kazuto
Sumita) acknowledge a Grant-in-Aid (#19530157) for Scientific Research (C) from the Ministry of
Education Culture, Sports, Science and Technology.
†
Corresponding author. Email address: seko@econ.keio.ac.jp.

11. Introduction
Japan is famous for its earthquakes. According to a recent survey, however, only 20% ofJapanese households purchased an earthquake insurance policy in 2005. Why do so many
households in Japan not purchase earthquake insurance policies given the high risk? And, what
are the implications of this risky behavior?
The low subscription rates for earthquake insurance have important policy implications not
only for Japan but also many other quake-prone countries. 1 First, and most importantly,
uninsured victims of major earthquakes may incur severe financial and non-financial losses,
which greatly influence the future well-being of these victims. Earthquake insurance can, atleast partly, cover these severe losses. Second, once a massive earthquake occurs, the prevalenceof uninsured individuals requires large recovery costs in the form of government grants andlow-interest loans to uninsured victims that are funded by all taxpayers.
Previous studies have analyzed the incidence of underinsurance against natural disasters
including earthquakes (Kunreuther, 1984). Basically earthquake insurance is fairly costly withhigh levels of deductions. Homeowners may be skeptical that their claims will be fullyrecognized and are aware of sweeping exclusions. And, if the earthquake is massive and damage
is devastating, there is always the risk that payouts might be limited and delayed. Further,ex-post government grants for victims create an immense moral hazard problem in the insurance
market. 2 Since inhabitants in quake-prone areas expect to receive grants, compensation and low
cost loans from the local and central governments after a massive earthquake, they have little
incentive to purchase insurance.
In addition to these reasons for low subscription rates, in this paper we focus on the current
1

For example, subscription rates for earthquake insurance are less than 11% in California (2000) and19.6% in Turkey (2006). Compared with these two countries and Japan, New Zealand has a compulsory
earthquake insurance system with a completely uniform premium setting.
2
This kind of moral hazard is called “charity hazard” in Browne and Hoyt (2000).

2

geographical risk rating in Japan’s earthquake insurance market. Because the Japanese
earthquake insurance system has extremely rough and crude geographical rating categories,
community uniform premiums are standardized and not linked to risk despite public perceptions
that some areas are much more prone to earthquakes than others. The community uniform
pricing requires cross-subsidies among individuals: individuals in risky areas will pay a
premium below their actuarial value at the expense of those in less risky areas. As a result,households in less risky areas do not purchase insurance policies and customers in relatively
high-risk areas purchase insurance. Thus, cross-subsidization creates a situation where only
those most at risk purchase insurance.
Although there are several studies that analyze cross-subsidization in health insurance(Pupp, 1981), to the best of our knowledge there are no previous studies of cross-subsidizationin earthquake insurance market. In general, catastrophes due to natural causes such as
earthquakes have distinctive characteristics: they occur infrequently and are unpredictable, but
can exact high costs due to their potential for devastating damage. This is the first econometricstudy to measure the degree and impact of cross-subsidization in earthquake insurance policy.
This paper is organized as follows: In section 2, we briefly describe the earthquake
insurance system in Japan and in section 3, we briefly review the related research. In section 4,
we introduce a simple theoretical model of insurance purchase under the community uniform
rating and define the concept of cross-subsidization. In section 5, we discuss the data set, theestimation results on the effect of the cross subsidization and the simulation results of theelimination of the cross subsidization. Section 6 presents the conclusions.

2. Earthquake Insurance System in Japan
In Japan, purchase of the earthquake insurance policies is voluntary, and is attached to fire
insurance in general. Earthquake insurance is provided under the auspices of the government.
3

Private companies sell earthquake insurance, but given the enormous potential amount of claims,
the Japanese government offers a reinsurance scheme and the government bears over 80 percentof the overall liability. 3 So the ultimate underwriter of earthquake insurance is the government,
not private companies. Under this system, the premiums are based on the government’s
regulations, not on private sector calculations.
A brief description of the Japanese earthquake insurance system is given as follows: Thecoverage of earthquake insurance policies is limited to buildings for residential use andhousehold goods affected by fire, destruction, burial or flood directly or indirectly caused by anearthquake, volcanic eruptions or tsunami. Claims are adjusted based on damage assessments. If
a building and/or household goods are totally destroyed the entire amount of insurance coverage
is paid and if the damage is assessed at half the building and/or household goods, 50% of theinsurance coverage is paid while partial losses are compensated at 5% of the insurance coverage.
The limit of insurance coverage is 50 million JPY for buildings and 10 million JPY forhousehold goods.
The potential scale of earthquake damages is so large that the government sets a limit on its
reinsurance exposure. Regulations specify the obligations of private insurance companies andthe government with the latter setting a limit of 5.5 trillion JPY as of September 2008 as
stipulated in the Earthquake Insurance Law (see Table 1 for detail). To put this figure into
context, the total claims paid out following the Kobe (Great Hanshin-Awaji) Earthquake totaled
78.3 billion JPY. 4
The earthquake insurance premium standard rates are composed of a basic rate and a3

Japan has a government-private shared policy for household risks as does California. Household risks inJapan are all reinsured in the Japanese Earthquake Reinsurance Company (JER) where losses are sharedby the insurers, the JER and the government, according to the total cost of damages. So this reinsurance
scheme offered by the government serves as an effective subsidy to the private insurance companies.
4
This figure is cited from the web site of the General Insurance Association of Japan on June 7th, 2008(http://www.sonpo.or.jp/archive/statistics/disaster/quake.html).

4discount rate. The basic rate is set as indicated in Table 1. In case a building was constructed
after June 1, 1981, a 10% discount on the cost of the premium is applied to the buildings orhousehold goods contained therein. This discount reflects stricter building standard regulations
instituted at that time. The premiums are based on the estimates of the likelihood of occurrence
and the expected damages of an earthquake. The likelihood of occurrence is estimated using therecords of massive earthquakes over the past 500 years. These estimates are computed at thegeographical level of prefectures, and each prefecture is classified into one of the four ratingzones (rank 1 (safest) to rank 4 (riskiest). See Table 1 for details). As a result, for typicalhousing, the insurance premiums per 100,000 JPY of coverage range from a low of 50 JPY in
the safest zone to a high of 175 JPY in the riskiest zone. 5 Thus for a 40 million JPY dwelling,
the annual premium could range from 20,000 to 70,000 JPY per annum.
Compared to other countries, the Japanese system is based on extremely rough and crude
geographical rating categories. For example, compared with only four risk rating zones in Japan,
California’s system is based on 19 risk rating zones (Jaffee and Russell, 2000). 6 Japan’s crude
risk ratings significantly distort the behavior of potential insurance customers, and distort
markets for earthquake insurance.
(Table 1 around here)

3. Literature Review
In this section we briefly review the related literature of the earthquake and crosssubsidization problem in the insurance market.
Naoi, Sumita and Seko (2007) implicitly showed the existence of cross-subsidization in theearthquake insurance market based on the estimated regional quality of life index (QOLI). Naoi,
5

Insurance premiums also vary according to the structure and construction method of the dwelling.
In October 2007, the Japanese government and the Non-Life Insurance Rating Organization of Japan(NLIRO) released a new insurance premium policy based on a new projection of earthquake probability.
However, the risk categories are still based on only four rating zones.

6

5

Seko and Sumita (2008) further examined the relationships between seismic risk and rental andowner-occupied housing prices in Japan.
Picard (2008) has theoretically investigated the role of private insurance in the prevention
and mitigation of natural disasters and shown that a competitive insurance market with actuarial
based rate determination and compensatory tax-subsidy transfers is better than regulated
uniform insurance pricing rules or state-funded assistance schemes.
Pupp (1981) explored the inextricable connection between community rating andcross-subsidies in health insurance and estimated total, family and individual cross-subsidies
based on a multivariate regression model by developing Pauly’s (1970) analysis that draws on
Arrow’s (1963) findings. Our study also builds on the findings of Browne and Hoyt (2000) who
estimated the demand function for flood insurance.
In this study, based on the data set used in the Naoi et al. (2007, 2008), we examine therelationship between the earthquake insurance purchasing decision and the cross-subsidies after
controlling various individual and housing characteristics.

4. The ModelIn this section, we present a simple analytical framework to illustrate household’s insurance
purchase decision. Previous studies have mainly focused on optimal contracts under asymmetric
information in a competitive insurance market. In comparison, our primary interest in this study
is on the effect of exogenous changes in insurance premium setting – actuarial and community
uniform premium – on the regional disparities in earthquake insurance participation. For thispurpose, we make the following assumptions: (1) the insurance premium is exogenously
determined by the government regulation, and (2) both customers and insurance companies
know the true risk of earthquake. The first assumption corresponds to the current Japanesesituation: the premiums are based on the government’s regulations, not on the private
6

company’s choices. 7 The second assumption implies that there is no information asymmetry inthis market. In general, individual customers can make a “preventive effort” against an
earthquake, e.g., having anti-seismic reinforcement to their dwelling. 8 If insurance companies
cannot observe this effort directly, adverse-selection problem would emerge (Laffont, 1989). Asa practical matter, however, insurance companies can partially observe customer’s effort, sincein Japan insurance premiums vary according to the quake-resistance quality of each housing
unit, as well as the customer’s location. 9
Suppose that there are two types of areas with differentiated risk of an earthquake. Some
individuals live in high-risk areas where the probability of an earthquake is, with 0

live in low-risk areas where the probability is

1.

For simplicity, we assume that all individuals suffer the same loss
earthquake. 10

in case of andenotes their endowed income, which is the same for everybody. Earthquake

insurance contracts specify the premium
earthquake

and the others,

and the indemnity

paid in case of an. If individuals buy earthquake insurance, they will haveearthquake occurs andincome in the two states is

if noin case of an earthquake. Without insurance their(“no earthquake”) and7(“earthquake”), respectively.

Rothschild and Stiglitz (1976) shows theoretically that, if insurance companies have imperfect
information about the accident probability, there will be underinsurance among low-risk customers (i.e.
low-risk customers will choose partial coverage insurance, while high-risk ones will have full coverage)
in a competitive insurance market with free entry.
8
Unobserved preventive effort will have important welfare implications. Leung (2001) theoreticallyshows that, in a dynamic general equilibrium context, full-coverage (social) insurance will reduce theequilibrium level of labor effort and hence will reduce overall social welfare. In a dynamic political
economy context, Leung et al. (2006) also show that, if individual effort can reduce the “loss” from a bad
event, the intensity of such effort will crucially affect the resulting economic growth and volatility.
9
Given the rough and crude geographical rating, customers also may not know their “true risk.” In such asituation, individuals make (and behave according to) estimates of their earthquake probabilities. In
general, the resulting equilibrium will critically depend on this informational assumption. However, if
low-risk customer’s (not necessarily true) estimates are actually lower than high-risk customer’s estimates,
our main results remain unchanged. The authors are very grateful for the referee on this point.
10
Ehrlich and Becker (1972) examine two alternatives to market insurance: self-insurance – a reductionin the size of a loss – and self-protection – a reduction in the probability of a loss. They show that market
insurance and self-insurance are substitutes. As a result, the degree of loss after the particular earthquake
would be smaller in riskier region. However, they also show that the incentive for self-insurance,compared with that for market insurance, is smaller for rare losses like earthquake.

7

An individual purchases an insurance contract in order to alter the pattern of income acrossdenote his income if there is no earthquake andtwo states. Let

his income if anearthquake occurs, and the expected utility function is given as follows:,,1
0 , thus

We assume that individuals are risk-averse

,

.

(1)

is quasi-concave.

Individual demand for earthquake insurance can be derived from equation (1). A contract,

determines the resulting pattern of income across two states and thus the expectedutility level,,,. From all the available contracts,,

the individual chooses the one that maximizes. He always has the option not to buy

any earthquake insurance. Hence an individual will purchase insurance only if,, where W , W,,

is the (uninsured) endowed income level in

two states.
As a benchmark, consider the case where insurance companies can offer different contracts
in two areas. We assume that the insurance contract should satisfy the following expectedzero-profit condition in each area: 11
,

1

.

(2)

Figure 1 illustrates the equilibrium outcome of this case. In Figure 1 the horizontal andvertical axes represent income in two states. The point E is the customer’s endowed income,. Zero-profit conditions given as equation (2) are shown as ZPCL and ZPCH in

Figure 1, respectively.
(Figure 1 around here)
Since individuals are risk-averse, typical customer’s indifference curve must be tangent tozero-profit line at a point like AL and AH in Figure 1 (yielding equal income in both states).
11

In terms of, , a zero-profit condition is explicitly given as 1
andyields equation (2).
Combining this equation with the definitions of

80.

The following two points should be mentioned here. First, each customer buys complete (full, definitions ofcoverage) insurance at fair actuarial premium. Since
immediately yields

andin equilibrium (complete insurance). In this case, zero-profit

condition (equation (2)) implies(fair actuarial premium). Second, even a risk

neutral customer would purchase this contract with actuarial premiums (i.e., customers should
prefer the point A to the point E regardless of their degree of risk aversion). Hence, wheninsurance companies can offer different contracts in low-risk and high-risk areas, every
individuals purchase insurance regardless of the location.
In the above benchmark case, insurance premiums are set so as to reflect the endowed risk
in each location (i.e. fair actuarial premium). However, in the current Japanese system, premium
levels do not fully reflect the regional earthquake risks, and regions with different earthquake
risk often have same premium level (i.e. community uniform premium).
Focusing on the complete insurance case, Figure 2 illustrates the typical customer’s choice
under community uniform premium. 12 Suppose that the fraction of low-risk customers is
Then the average earthquake probability of the customers is

1

. 13

. The

insurance contract, which is common to both areas, should lie on the following market
zero-profit line (ZPC in Figure 2):
.

1

(3)

The income pattern represented by the point A requires cross-subsidies among customers:
customers in high-risk areas will pay a premium below their actuarial value at the expense of

12

Restricting customer’s choice to the complete contract is not necessary for our results here. If
customers can choose the optimal insurance contract, less risk-averse customers would prefer smaller
insurance coverage. However, with a fixed loading cost, some of these customers in low-risk areas must
prefer not to purchase insurance.
13
Note that, if some low-risk customers choose not to purchase insurance,is endogenously
determined in equilibrium. With some regularity condition on the distribution of heterogeneous customers(with respect to their degree of risk-aversion), we can show thatis uniquely determined in equilibrium.

9

those in low- risk areas. 14 The uniform premium should bepremiums,

should be somewhere between

and. Compared with actuarial(i.e.

). The per-capita

subsidy for the customers in high-risk areas is defined as
for those in low-risk areas isand the per-capita tax.
(Figure 2 around here)

As shown in the benchmark case, actuarially fair premium setting predicts every
individuals, regardless of their location, purchase insurance. In contrast, the premium settingthat is constant across regions predicts that not all individuals in low-risk areas purchaseinsurance. Figure 3 shows that the low-risk customer who has a flatter indifference curve (i.e.,less risk-averse)

will be indifferent between complete insurance (the point A) and theendowed income without any insurance (the point E). Hence individuals who are lessrisk-averse than this marginal customer would not purchase insurance. In comparison,
individuals in high-risk areas always purchase insurance regardless of their degree of risk
aversion.
(Figure 3 around here)
Figure 3 also indicates that larger cross-subsidies across regions lead to fewer insurance
purchase in low-risk areas. For example, holding other factors constant, higher earthquake
probability in high-risk areas
probability

should be associated with higher average earthquake. This immediately leads to higher uniform premium

cross-taxes in low-risk areas. At the same time, since higher

and larger per-capita

makes the market zero-profit

line ZPC flatter, this results in lower subscription rate in low-risk areas. 15 In the following
14

In a competitive market without any government regulations, cross-subsidization would disappear
through cream skimming. Because a firm can earn positive profit by offering low-risk customers (who arepaying a premium above their actuarial value) a cheaper insurance, cream skimming leads to separating
equilibria in which different types of customers purchase different contracts (Rothschild and Stiglitz,1976).
15
In this model, we do not allow individuals to move across regions. Allowing for individual mobility

10empirical section, we directly test this hypothesis using most recently available dataset ofJapanese households. 16

5. Estimation
5.1 Data
The Keio Household Panel Survey (KHPS), sponsored by the Ministry of Education, Culture,
Sports, Science and Technology, is the first comprehensive panel survey of households in Japan,
conducted annually by Keio University since 2004. In the KHPS, we can use not only basic
information about respondent’s social and demographic characteristics, but also information
regarding their residential locations and purchases of earthquake insurance policies. In the firstwave, self-administered questionnaires were given to 4,005 respondents, male and female, aged
20-69 years. These respondents were selected by stratified two-stage random sampling. In thefollowing analysis, five waves of the KHPS (2004–2008) are utilized to examine thehousehold’s insurance purchase decision, with special emphasis on the effect ofcross-subsidization across regions.
In addition to the KHPS, the fair actuarial premium and the resulting cross-subsidies arecalculated based on the objective estimates of earthquake probability. The earthquake
probability measure is taken from the Probabilistic Seismic Hazard Map (PSHM) provided by
the National Research Institute for Earth Science and Disaster Prevention (NIED). 17 The PSHM
provides the probability of earthquake occurrence for the likely range of seismic intensity. In thewith certain costs may yields similar results, and is an interesting direction for future extension. Picard(2008) presents a model with individual mobility, but in that insurance purchase is compulsory.
16
Moreover, since a part of individuals in less risky areas do not purchase insurance policies andcustomers in high-risk areas still stay in the market, uniform pricing raises the overall cost of earthquake
insurance: this further makes inhabitants in low-risk areas reluctant to protect themselves against
earthquakes through the purchase of insurance policies.
17
The original PSHM data is provided as the ESRI grid format, where grid cells are defined as
geographic space of equally sized square grid points. The PSHM data gives the earthquake probabilities
for every 1km × 1km grid cells all over Japan. In the following analysis, we aggregate the original dataand construct the city-level averages in order to match the PSHM probability with the KHPS. The original
data is available at http://www.j-shis.bosai.go.jp/.

11following analysis, we use the occurrence probability of earthquakes with ground motions equal
to or larger than JMA seismic intensity 6

within 30 years. 18 Probability of earthquake

occurrence obtained from the PSHM is summarized in Figure 4.
(Figure 4 around here)
Based on the PSHM 30-years probability
annualized probability of earthquake occurrence as

described above, we calculate the11/. 19 We assume thatthe earthquake probability taken from the PSHM is the proxy for the true risk of earthquakes
and calculate the fair actuarial premium based on the PSHM earthquake occurrence
probability. 20 For an indemnity of 10 million JPY, the fair actuarial premium is calculated as
10,000,000. In the following analysis the fair actuarial premium is adjusted so that it
has the same sample mean as the observed community rate. 21 The distribution of unadjusted
actuarial premium and that of observed community uniform premium are shown in Figure 5.
Figure 5 indicates that the calculated actuarial premium is unevenly distributed across regions,while the community premium is centered around its mean. It also suggests that, due to theextremely high levels of actuarial premium in some regions, the average actuarial values are
somewhat higher than the observed community rates.
(Figure 5 around here)
18

The Japan Meteorological Agency (JMA) seismic intensity scale, which is measured with a seismic
intensity meter, and is graded from 0 to 7, provides a measure of the strength of seismic motion. For full
explanation of the JMA seismic intensity scale, see http://www.jma.go.jp/jma/kishou/know/shindo/
explane.html. In general, the relationship between the JMA scale and the Richter scale depends on a
distance from the epicenter. Even an earthquake with a small intensity on the Richter scale can have alarge JMA intensity at locations near the epicenter.
19
Assuming that the earthquake probabilities are constant over time,andmust satisfy the∑. This yields our measure of annualized earthquake
1
following relationship.
probability.
20
In our recent paper, we carefully examine the empirical validity of this assumption, and find that thebias stemming from the use of objective PSHM probability as a proxy for individual risk assessments isalmost negligible (Naoi et al., 2008).
21
Since the actual insurance contracts have high levels of deductions (3% of property value), and a total
claim payment limit (5.5 trillion JPY), the average premiums of actual contracts tend to be lower thanactuarial ones. In consideration of these factors, the actuarial premium is adjusted to have the same
sample mean as the observed community rate.

12

Observed community uniform premiums are based on NLIRO insurance rates for wooden
housing without any anti-seismic construction method. As explained in Section 2, community
rates are set at the geographical level of prefectures, and each prefecture is classified into one of
the four rating zones. In the following analysis, we use the insurance premiums per 10 million
JPY of coverage, which range from a low of 12 thousand JPY in the safest zone to a high of
35.5 thousand JPY in the riskiest zone. 22 Premium discounts for a building constructed under
the stricter building code and for long-term contracts are also applied to the above basic rates.
Finally, we define the cross-subsidization
premiumas the difference between the fair actuarial

and the observed community rate,

. Clearly, since theactuarial premium is directly linked to the PSHM probability, risky areas will have a subsidized
uniform premium with

0 and less risky areas will have taxed premium with0.

Our theoretical prediction suggests that larger cross-subsidies across regions (i.e. larger negativevalues of) lead to fewer insurance purchase in low-risk areas. Hence we expect thathas positive impact on the household insurance purchase decision. Further, because the model
also predicts that cross-subsidies do not have any impact on the insurance purchase in high-riskareas, we also define the modified cross-subsidization measureifwhich equals toand 0 otherwise.
Table 2 presents definitions and summary statistics of main variables used in our statisticalanalysis. It also provides sample means of variables both for insured and uninsured households.
A simple t-test of sample means (“Group Mean Comparison”) shows that there is significant
difference in measured cross-subsidies between insured and uninsured households. While
insured households tend to pay a subsidized premium below their actuarial value (i.e.,
220),These basic rates are as of September, 2007. As explained in footnote 5, NLIRO released a new
insurance premium policy in October, 2007. To check whether this policy change has any influence on
our empirical results, we estimated the model without 2008 sample, and found that there are no
fundamental changes in our estimates.

13

uninsured households face taxed premium higher than their actuarial value (i.e.,0).

(Table 2 around here)

5.2 Estimation Results
In order to test the effect of cross-subsidization on the purchase of earthquake insurance, weestimate the binary probit model. We use the cross-subsidization variable
modified version

and its

to measure the extent of cross-subsidization. If cross-subsidization

really matters, the coefficients ofandare expected to show a positive impact. For thecost variable, we use the observed community rates. The coefficient of this variable is expected
to show a negative impact.
Except for cross-subsidy measures and insurance premiums, variables related to respondentand housing characteristics are included in our model. For the respondent characteristics, thefollowing variables are used: age, years of education, marital status (married = 1) and annual
household income. For the housing characteristics and other control variables, the following
categorical dummies are included: building type of housing, ownership of housing, size of cityand region in which respondent resides, and dummies for survey years.
Table 3 presents the probit results of a household’s insurance purchase. The dependent
variable is one if the household buys an earthquake insurance policy. The coefficient ofisfound to be positive and significant (Model [1]). This indicates that in the Japanese earthquake
insurance market, cross-subsidies across areas discourage inhabitants in low-risk areas frompurchasing insurance policies, as our model predicts. The coefficient of the community uniform
rate is negative and significant as expected. For renter households, we also find that the priceeffect is largely attenuated (i.e., the interaction term between renter dummy and community
uniform rate has significantly positive impact on their insurance purchase). This may attribute to
the limited coverage of insurance for renter households: the coverage of earthquake insurance14policies is limited to household goods for renter households, while for homeowners insurance
covers buildings for residential use as well. 23
Further, since the effect of cross-subsidization might be asymmetric between subsidized
regions

0 and taxed regions

cross-subsidization measure

0 , we estimate the model with the modified

in Model [2]. The result also indicates that the cross-taxes in) lead to underinsurance in these areas. But

low-risk areas (i.e. the larger negative values ofin this case the estimated coefficient ofis much larger than that ofin Model [1],which is consistent with our prediction that the cross-subsidization does not matter in high-riskareas.
(Table 3 around here)
As for the building type of housing, the coefficient of condominium shows a positively
significant impact. This is because condominiums, especially in tall buildings, tend to suffer
larger damages than detached housing. Regarding the regional dummies, Kanto, Chubu andChugoku area dummies show a positively significant impact (results not shown). These regionaldummies would capture regional economic conditions or the effects of region-specificenvironments.
Since the household decision to purchase earthquake insurance is likely to be influenced byunobserved heterogeneity such as attitudes toward risk, we have also estimated the model by the
random-effect probit. The results, however, show qualitatively similar estimated coefficients.
Notably, the coefficients of theandshow the same positive sign with the probit

estimate (Models [3] and [4]).

5.3 Simulation
To examine the effect of cross-subsidization on the overall subscription rates for earthquake23

We also examined the differential effect of our cross-subsidization variable between homeowners andrenter households, but find no significant difference between these two groups.

15

insurance, Table 4 illustrates the simulation results based on the probit model presented in theprevious section (Model [2]). The first column shows the observed PSHM earthquake
probability. The second column (“observed subscription rates”) shows the observed proportionof households holding insurance policies in the KHPS. The third column (“subscription rates
under actuarial premium”), calculated from our estimation result, shows the predictedprobability of holding insurance policies under the actuarial premium without any
cross-subsidization.
(Table 4 around here)
The predicted probabilities are obtained by using actuarial premiums instead of observed
ones, and setting

0 in Model [2] presented in Table 3. As a result, the observed

subscription rate of 24.2% is considerably increased under the actuarial premium without any
cross-subsidization to 27.9%. Furthermore, increases in the subscription rates are particularly
prominent in regions with low earthquake risk, which is also consistent with our theoreticalprediction. The increase in the subscription rate ranges from 1.9 percentage point in the riskiest
prefectures (rank 4) to 6.3 percentage point in the least risky prefectures (rank 1).

6. Conclusion
The reason why so many Japanese households do not purchase earthquake insurance is because
it is too expensive. For those who face relatively less risk, the community uniform pricing
system inflates premiums. For those who are at high risk, the absolute high cost of insurance
ensures that many who ought to buy insurance tend not to. Even if people are risk averse,
catastrophic earthquakes are rare events, even in Japan, and thus many people take their chancesand save a lot on premiums.
A theoretical model is presented to show the connection between community uniform
rating and cross-subsidies in earthquake insurance policy in Japan. Cross-subsidies are defined16

as the difference between a fair actuarial premium and the community uniform rate. The
estimation results show that the uniform community rating may unintentionally cross-subsidize
inhabitants in high risk areas at the expense of inhabitants in low risk areas. That is, the current
Japanese earthquake insurance system actually lowers overall subscription rates, althoughpolicy makers are seemingly unaware that this is the case. Our simulation results indicate that
replacing the current community rating with the fair actuarial premium would increase theoverall subscription rate for earthquake insurance by about 3.7 percentage point, and that theincrease is particularly prominent in relatively less risky areas. We propose modifying theJapanese earthquake insurance system by adopting a more refined risk rating system that moreclosely reflects regional differences in earthquake risk and set premiums accordingly.

References[1] Arrow, K. (1963), “Uncertainty and the Welfare Economics of Medical Care,” American
Economic Review, 53(5), pp.941-973.
[2] Browne, M.J. and R.E. Hoyt (2000), “The Demand for Flood Insurance: Empirical
Evidence,” Journal of Risk and Uncertainty, 20(3), pp.291-306.
[3] Ehrlich, I. and G.S. Becker (1972), “Market Insurance, Self-Insurance, and Self-Protection,”
Journal of Political Economy, 80(4), pp.623-648.
[4] Jaffee, D.M. and Russel, T. (2000), “Behavioral models of insurance: The case of the
California Earthquake Authority,” Paper presented at the NBER Insurance ProjectWorkshop.
[5] Kunreuther, H. (1984), “Causes of Underinsurance against Natural Disasters,” Geneva
Papers on Risk and Insurance, 9(31), pp.206-220.
[6] Laffont, J.J. (1989), The Economics of Uncertainty and Information, Cambridge, MA: MIT
Press.
17[7] Leung, C.K.Y. (2001), “Productivity Growth, Increasing Income Inequality and Social
Insurance: The Case of China?,” Journal of Economic Behavior and Organization, 46(6),pp.395-408.
[8] Leung, C.K.Y., S.H.K. Tang and N. Groenewold (2006), “Growth Volatility and Technical
Progress: A Simple Rent-Seeking Model,” Journal of Economics (Zeitschrift für
Nationalökonomie), 88(2), pp.159-178.
[9] Naoi, M., K. Sumita and M. Seko (2007), “Earthquakes and the Quality of Life in Japan,”
Journal of Property Research, 24(4). pp.313-334.
[10] Naoi, M., M. Seko and K. Sumita (2008), “Earthquake Risk and Housing Prices in Japan:
Evidence Before and After Massive Earthquakes,” Paper presented at the Macroeconomics,
Real Estate, and Public Policy workshop in Istanbul, Turkey, July, 2008.
[11] Pauly, M.V. (1970), “The Welfare Economics of Community Rating,” Journal of Risk andInsurance, 37(2), pp.407-418.
[12] Picard, P. (2008), “Natural Disaster Insurance and the Equity-Efficiency Trade-Off,”
Journal of Risk and Insurance, 75(1), pp.17-38.
[13] Pupp, R.L. (1981), “Community Rating and Cross-Subsidization in Health Insurance,”
Journal of Risk and Insurance, 48(4), pp.610-627.
[14] Rothschild, M. and J. Stiglitz (1976), “Equilibrium in Competitive Insurance Markets: An
Essay on the Economics of Imperfect Information,” Quarterly Journal of Economics, 90(4),pp.629-649.

18

Figure 1: Insurance Demand under Fair Actuarial Premium

Figure 2: Insurance Demand under Community Uniform Premium

19Figure 3: Insurance Demand and Degree of Risk Aversion

Figure 4: Earthquake Occurrence Probability by Prefecture

20

21

0

20000

60000

Annual Insurance Premium (in JPY)

40000

Fair Actuarial Premium

80000

100000Community Uniform Premium

0.00E+00
1200001.00E-05

2 .00 E-05

3 .00 E-05

4 .00 E-05

5 .00 E-05

6 .00 E-05

7 .00 E-05

8 .00 E-05

Notes: Premium discounts for a building constructed under the stricter building code and for long-term contracts are applied to community uniform rates.
Observations with calculated actuarial values above 100,000 JPY are excluded. Estimated kernel densities for actuarial and uniform premiums areshown on the left and right axis, respectively.

0.00E+00-200005.00E-06

1.00E-05

1.50E-05

2.00E-05

2.50E-05

3.00E-05

3.50E-05

Figure 5: Distribution of Fair Actuarial Premium and Community Uniform PremiumTable 1: Earthquake Insurance System in Japan

Coverage
Risk covered
Coverage conditions(% paid for the amount insured)
Limit of insurable amountParticipation method
Limit of total payment
Premium(per 1,000 yen amount insured)
Rank 1: safest
Rank 4: riskiest
Premium discounts
Rating method
Risk rating method

Class location

Details
Buildings for residential use and household goods
Earthquake, volcanic eruptions and tsunami
Buildings and household goods: total loss (100%) / half loss (50%) / partial loss (5%)
Buildings: 50 million yen
Household goods: 10 million yen
Attached to the fire insurance
5.5 trillion yen for a single earthquake
Rank 1: 0.50 (non-wooden building) / 1.20 (wooden building)
Rank 2: 0.70 / 1.65
Rank 3: 1.35 / 2.35
Rank 4: 1.75 / 3.55
New building code discount: 10% discount for buildings constructed after June 1, 1981
Based on the estimates of the likelihood of occurrence and the expected damages ofan earthquake
Based on the records of massive earthquakes over the past 506 years
Rank 1: Hokkaido, Fukushima, Shimane, Okayama, Hiroshima, Yamaguchi,
Kagawa, Fukuoka, Saga, Kagoshima, Okinawa
Rank 2: Aomori, Iwate, Miyagi, Akita, Yamagata, Ibaragi, Tochigi, Gunma,
Niigata, Toyama, Ishikawa, Yamanashi, Tottori, Tokushima, Ehime,
Kochi, Nagasaki, Kumamoto, Oita, Miyazaki
Rank 3: Saitama, Chiba, Fukui, Nagano, Gifu, Aichi, Mie, Shiga, Kyoto,
Osaka, Hyogo, Nara, Wakayama
Rank 4: Tokyo, Kanagawa, Shizuoka
100%
Liability of government
50%

Reinsurance scheme

Liability of insurance co.
110bil.

1.73tril.
Total Payment Claim

5%5.5tril.

Notes : In October 2007, the Japanese government and the Non-Life Insurance Rating Organization of Japan (NLIRO) released a new
insurance premium policy based on a new projection of earthquake probability. Above explanations for premium rating and classlocation are as of September 2007.

22

Table 2: Summary Statistics
Variables
Holding earthquake insurance policy (Yes = 1)
Cross-subsidy (CS)Modified cross-subsidy (= 0 if CS > 0)
Community uniform premium
Actuarial premium
Annual earthquake probability
Age
Years of education
Married (Yes = 1)
Annual household income (in 10 thousand JPY)
Type of housing
Detached house (Yes = 1)
Row house (Yes = 1)
Condominium (Yes = 1)
Apartment (Yes = 1)
Ownership of housing
Homeowner (Yes = 1)
Private renter (Yes = 1)
Public renter (Yes = 1)
Living in company housing (Yes = 1)
Number of Obs.

Full Sample
Mean
0.242
0.000
-27957.1
20021.0
20021.0
0.006
48.85213.0650.783
687.237

Sample Means
InsuredMean
111408.2-25271.2
30617.4
30617.4
0.008
50.57313.0350.842
762.557

UninsuredMean
0-3644.0-28815.0
16636.3
16636.3
0.006
48.30213.0750.765
663.179

Group mean
comparison(P-values)

0.779
0.018
0.171
0.032

0.871
0.013
0.111
0.005

0.749
0.020
0.190
0.041

(0.000 ) †(0.008 ) †(0.000 ) †(0.000 ) †

0.841
0.108
0.034
0.017
12,607

0.989
0.008
0.001
0.002
3,052

0.793
0.141
0.045
0.021
9,555

(0.000 ) †(0.000 ) †(0.000 ) †(0.000 ) †(0.000 ) †(0.000 )(0.000 ) †(0.000 ) †(0.000 ) †(0.000 ) †(0.364 )(0.000 ) †(0.000 ) †Notes : The actuarial premium is normalized to have same sample average as the observed premium. “ Group mean comparison ”
represents p-value of paired t-test of equal means between insured and uninsured. If the two means have different variances, the test is
conducted using Welch’s approximation. † indicates that two sample means have different variances.

23

Table 3: Probit Models of Earthquake Insurance Purchase[1]
ProbitModel
Holding earthquake insurance policy (Yes =1)
Cross subsidy (CS) (x 10,000)
Modified cross subsidy (= 0 if CS > 0) (x 10,000)
Community uniform premium (x 10,000)
Community uniform premium x Renter (Yes = 1) (x 10,000)
Age
Years of education
Married (Yes = 1)
Self-employed (Yes = 1)
Annual household income
Type of housing
Detached house (Yes = 1)
Row house (Yes = 1)
Condominium (Yes = 1)
Apartment (Yes = 1)
Ownership of housing
Homeowner (Yes = 1)
Private renter (Yes = 1)
Public renter (Yes = 1)
Living in company housing (Yes = 1)
Dummy variables
RegionCity sizeYear
Log-likelihood
Number of Obs.

[2]
ProbitCoef.
0.0159(S.E.)(0.0017) **-0.37100.29300.00170.00080.1922-0.09610.0001**(0.0282)(0.0823) **(0.0011)(0.0068)(0.0352) **(0.0312) **(0.0000) **Coef.

(S.E.)

0.0722-0.3530
0.29800.00180.00080.1896-0.09230.0001(0.0073) **(0.0281) **(0.0857) **(0.0011)(0.0068)(0.0352) **(0.0311) **(0.0000) **(Omitted Category)
0.1286(0.1130)
0.2120(0.0454) **0.3411(0.1536) *(Omitted Category)
0.1278(0.1144)0.2028(0.0457) **0.3400(0.1542) *(Omitted Category)-2.2628(0.2122) **-2.5535(0.2741) **-2.2171(0.2575) **(Omitted Category)-2.2859(0.2191) **-2.5265(0.2790) **-2.2400(0.2637) **

Yes
Yes
Yes
-6275.6
12,607Yes
Yes
Yes-6267.4
12,607

Notes : Robust standard errors are reported for probit models. **: significant at 1%, *: significant at 5%, +: significant at 10%.

24

Table 3: Probit Models of Earthquake Insurance Purchase (Continued)[3]
Random-effect Probit
Coef.
(S.E.)
0.0365(0.0074) **Model
Holding earthquake insurance policy (Yes =1)
Cross subsidy (CS) (x 10,000)
Modified cross subsidy (= 0 if CS > 0) (x 10,000)
Community uniform premium (x 10,000)
Community uniform premium x Renter (Yes = 1) (x 10,000)
Age
Years of education
Married (Yes = 1)
Self-employed (Yes = 1)
Annual household income
Type of housing
Detached house (Yes = 1)
Row house (Yes = 1)
Condominium (Yes = 1)
Apartment (Yes = 1)
Ownership of housing
Homeowner (Yes = 1)
Private renter (Yes = 1)
Public renter (Yes = 1)
Living in company housing (Yes = 1)

-0.86800.73800.00420.00950.4493-0.07150.0002

2

Variance of random effects (σ ):22(0.1040)(0.2290) **(0.0050)(0.0298)(0.1425) **(0.1030)(0.0001) **0.1450-0.8060
0.74100.00420.00860.4447-0.06280.0002(0.0312) **(0.1000) **(0.2290) **(0.0050)(0.0298)(0.1424) **(0.1029)(0.0001) *(Omitted Category)
0.5719(0.4526)
0.3552(0.1863) +0.5281(0.4367)(Omitted Category)
0.5531(0.4513)0.3337(0.1864) +0.5156(0.4372)(Omitted Category)-4.9222(0.5694) **-5.4469(0.6924) **-4.5310(0.6884) **2.6527(0.0569)(Omitted Category)-4.9491(0.5707) **-5.3390(0.6866) **-4.5446(0.6922) **2.6492(0.0570)0.8756

ρ = σ / (σ + 1)
Dummy variables
RegionCity sizeYear
Log-likelihood
Number of Obs.

**

[4]
Random-effect Probit
Coef.
(S.E.)(0.0047) ‡0.8753

Yes
Yes
Yes-3628.2
12,607(0.0047) ‡

Yes
Yes
Yes
-3629.4
12,6072

Notes : **: significant at 1%, *: significant at 5%, +: significant at 10%. σ represents the random-effect variance component and ρ represents
the proportion of the total variance contributed by the random-effect variance component. ‡ indicates that the likelihood-ratio test of ρ = 0 is
rejected at 1% significance level.

Table 4: Simulation Results – Subscription Rates under Actuarial Premium

All Japan
Rating Zones
Rank 1 (Safest)
Rank 2
Rank 3
Rank 4 (Riskiest)

Observed
Earthquake Probability
0.65%

Observed
Subscription Rates
24.2%

Predicted Subscription Rates
under Actuarial Premium
27.9%

0.08%
0.22%
0.81%
1.21%

23.9%
23.3%
23.2%
26.6%

30.2%
29.1%
25.3%
28.5%

Notes : Simulation results are based on Model [2] estimates presented in Table 3.

25